Class NEET 2026 ALL Q #1912
COMPETENCY BASED
APPLY
4 Marks 2026 NTA-RE-NEET-2026 MCQ SINGLE
An ac voltage $V=220~sin(2\times10^{3}t)$ Volt is applied to a series LCR circuit. Then the current amplitude in this circuit is: (Given: $L=10~mH.$ $C=25\mu F,$ $R=100~\Omega)$
(A) 22.0 A
(B) 2.2 A
(C) 5.5 A
(D) 11.0 A
Correct Answer: B

AI Tutor Explanation

Powered by Gemini

Detailed Solution

Step 1: Identify given parameters

From the voltage equation $V = 220 \sin(2 \times 10^3 t)$, we identify the peak voltage $V_0 = 220 \text{ V}$ and angular frequency $\omega = 2 \times 10^3 \text{ rad/s}$. Given components are $L = 10 \text{ mH} = 10^{-2} \text{ H}$, $C = 25 \mu\text{F} = 25 \times 10^{-6} \text{ F}$, and $R = 100 \Omega$.

Step 2: Calculate Inductive and Capacitive Reactance

Inductive reactance $X_L = \omega L = (2 \times 10^3) \times (10^{-2}) = 20 \Omega$.
Capacitive reactance $X_C = \frac{1}{\omega C} = \frac{1}{(2 \times 10^3) \times (25 \times 10^{-6})} = \frac{1}{0.05} = 20 \Omega$.

Step 3: Determine Impedance

Since $X_L = X_C$, the circuit is in resonance. The impedance $Z$ is equal to the resistance $R$.
$$Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{100^2 + (20 - 20)^2} = 100 \Omega$$

Step 4: Calculate Current Amplitude

The current amplitude $I_0$ is given by:
$$I_0 = \frac{V_0}{Z} = \frac{220}{100} = 2.2 \text{ A}$$

Final Answer: 2.2 A

AI generated content. Review strictly for academic accuracy.

Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must identify the resonance condition from the given parameters and apply the impedance formula for an LCR circuit.
Knowledge Dimension: PROCEDURAL
Justification: The student follows a specific sequence of calculations (reactance, impedance, Ohm's law) to reach the solution.
Syllabus Audit: In the context of NEET, this is classified as COMPETENCY. It tests the ability to recognize resonance in AC circuits, a high-frequency topic in competitive physics.